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Baye Morgan Scholten (2006) - Information Search and Price Dispersion (view source)
Revision as of 21:41, 25 January 2010
, 21:41, 25 January 2010no edit summary
Taking the derivitive with respect to <math>p\,</math>:
<center>
<math>\frac{d(v(M,p))}{dp} = \frac{dv\partial v(M,p)}{dm\partial m} \cdot \frac{dM\partial M}{dp\partial p} + \frac{dv\partial v(M,p)}{dp\partial p} = 0,\,</math> where<math>\frac{dM\partial M}{dp\partial p} = \frac{de\partial e(p,u)}{dp\partial p}\,</math>.
<math>\therefore q(m,p) = \frac{de\partial e(p,u)}{dp\partial p} = -\frac{\frac{dv\partial v(M,p)}{dp\partial p}}{\frac{dv\partial v(M,p)}{dm\partial m}}\,</math>
<math>\therefore q(m,p) = -\frac{d}{dp(v(p))}\,</math> in our case.
<center>
'''Fixed sample search'''
In a fixed sample search the consumer commits to conducting <math>n\,</math> searches
and then buys from the firm offering the lowest price
The consumer seeks to minimize the expected cost (purchase + search) given by:
<center><math>\mathbb{E}(C) = K E(p_{min}^{(n)}) + cn\,</math> </center>
<center>where <math>E(p_{min}^{(n)}) = E(min\{p_1,p_2,\ldots,p_n\}) \,</math> </center>
The distribution of the lowest <math>n\,</math> draws is: <center><math>F_{min}^{(n)}(p) = 1 - (1-F(p))^n\,</math> </center>
\therefore
<math>
